Yes, it possible: all sites will have same users, so no matter where you can register - you can login in any site.

MySQL users of slave sites should have access to database of main site. Each site can either use own files or use same files for all sites (parked domains).

1) Does each site have its own admin panel to edit menus, forums, etc for that site only?

Yes, each site has own admin panel as usual. All other database data except users will be unique per site as usual.

2) Can I make someone an admin of just one the sites without giving them full access to all sites?

You can create a separate usergroup for each site, next assign usergroup to particular user and login permission in Joomla global configuration. So i.e. only users with assigned usergroup 'Site A admins' will be able to login in site A.

When you say use own files, I'm unsure what you are saying. I want to share the users for single login, comments, etc. The only thing that would be shared is if the write in the forums of slave, and someone responds, they can see that when on master site. Or if they click my groups, my events in jomsocial from master, they see events that were created on slaves.

I don't want to have to purchase a domain for each site it possible. I am content with either